The tech boom in Manhattan office space is creating a space crunch that has building owners cranking up rents.

The smaller and most desirable Midtown South office market has the lowest vacancy rate, hovering at 6 percent, and an asking rent of $63.04 per square foot — up 5 percent year over year.

In Midtown, average asking rents are up 7 percent from the year-earlier period, to $74.27 per foot.

To satisfy both immediate and future needs, the tech companies also are gobbling up space downtown. That has buildings raising asking rents at an unprecedented rate.

A new CBRE report has found building owners boosted downtown office rents 4 percent to $48.70 per square foot, from $46.47 in the beginning of the year.

“Leasing is strong and the tenants are accepting the pricing,” according to Sheldon Cohen, who heads CBRE’s downtown office.

Amazon, AppNexus, Facebook, Spotify, eBay, ZocDoc, LinkedIn and Yahoo! have added the most city jobs in the last quarter, CBRE’s Sacha Zarba said. That also reflects recent space additions.

From 2008 to the end of last year, growth leader AppNexus, the Web advertising giant, expanded 8,596.4 percent from occupying 2,520 square feet to 219,150 square feet.

Among others, LinkedIn went from 6,000 square feet, to 170,000 square feet, or 2,733.3 percent, and Facebook from 10,000 square feet to 154,153 square feet, or 1,441.5 percent. By comparison, Twitter was a mere piker, growing from 11,000 square feet to 140,000 square feet, or 1,172.7 percent.

Amazon, however, will be the square-foot growth giant, as it is still seeking 300,000 square feet with short-term expansions expected to boost that to 500,000 square feet.

“We are getting to the point where the operational side is more important than the cultural side,” said CBRE’s Peter Turchin of space searches beyond Midtown South, as the expansive pace of hiring has caused companies to need space immediately — and not in the typical growth pattern of one to five years.